C2/L3B_monte_carlo.ipynb

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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt \n",
    "import pandas as pd \n",
    "from collections import defaultdict\n",
    "\n",
    "import sys\n",
    "sys.path.insert(0, '..')\n",
    "from utils.plot_lib import set_default\n",
    "\n",
    "set_default(figsize=(6, 4))"
   ]
  },
  {
   "source": [
    "This script is based on [this](https://d3c33hcgiwev3.cloudfront.net/_e6b9ab92bcaef99f2a96d0f08c0b51a3_lesson_03.html?Expires=1619049600&Signature=BoxJ0FB2gDXjdB6h~jJgvpVXVuehASTZnVpSiaee6PiDhNRbHAaoQZgVCpxaWRiqM1TOcuoCO5foaZcdIrB1M9BvaUtshmaeuseU-8VIU~f3Z7vY3VYngFSfb84gJpdtg8iTQplGzd1BKIRILX8IX9VD7TBWcsrt3RFEL1VVSQQ_&Key-Pair-Id=APKAJLTNE6QMUY6HBC5A).\n",
    "\n",
    "### Monte carlo simulation \n",
    "\n",
    "Monte Carlo estimation refers to simulating hypothetical draws from a probability distribution in order to calculate important quantities. These quantities might include the mean, the variance, the probability of some event, or quantiles of the distribution. All of these calculations involve integration, which except for the simplest distributions, can be very difficult or impossible.\n",
    "\n",
    "Suppose we have a random variable $\\theta$ that follows:\n",
    "\n",
    "$\\theta \\sim Gamma(a, b)$\n",
    "\n",
    "$a = 2 \\text{ and } b = \\frac{1}{3}$\n",
    "\n",
    "Where: \n",
    "\n",
    "$\\mathbb{E}(\\theta) = \\frac{a}{b} = 6$\n"
   ],
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   "execution_count": 16,
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   "outputs": [],
   "source": [
    "from scipy.stats import gamma\n",
    "\n",
    "a, b = 2, 1/3 # Gamma function parameters\n",
    "m = 10000 # Monte carlo sample size\n",
    "\n",
    "# Lambda is 1/scale\n",
    "rv = gamma(a, loc = 0., scale = 1/b)"
   ]
  },
  {
   "source": [
    "If we have a random sample from a distribution, the average of those samples converges in probability to the true mean of that distribution by the Law of Large Numbers. Furthermore, by the Central Limit Theorem (CLT), this sample mean can be written as:\n",
    "\n",
    "$ \\bar{\\theta}^* = \\frac{1}{m}\\sum_{i=1}^m \\theta_i^* $\n",
    "\n",
    "It is also possible to approximate this variance with the sample variance:\n",
    "\n",
    "$ \\hat{Var(\\theta)} = \\frac{1}{m}\\sum_{i=1}^m (\\theta_i^* - \\bar{\\theta}^*)^2 $"
   ],
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   "execution_count": 18,
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     "text": [
      "The first 6 theta values are: [ 6.95464211 10.08906831  8.0512179  14.91576443  6.18135974  4.27878415]\n"
     ]
    }
   ],
   "source": [
    "# sampling from gamma function\n",
    "theta = rv.rvs(m)\n",
    "print('The first 6 theta values are: {}'.format(theta[:6]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
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\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "# Plotting the histogram of the random samples\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.hist(theta, density=True, histtype='stepfilled', alpha=0.2)\n",
    "# Sampling in all the domain of the function\n",
    "x = np.linspace(rv.ppf(0.01),rv.ppf(0.99), m)\n",
    "ax.plot(x, rv.pdf(x), 'r-', lw=5, alpha=0.6, label='gamma pdf')\n",
    "ax.legend(loc='best', frameon=False)\n",
    "plt.title('Histogram of theta')\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "A monte carlo approximation to the expected value of $\\theta$ is: $"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "The Monte carlo approximation for the mean is 5.980474582771642\nThe true value for the mean is 6.0\n"
     ]
    }
   ],
   "source": [
    "print('The Monte carlo approximation for the mean is {}'.format(np.mean(theta)))\n",
    "print('The true value for the mean is {}'.format(a / b))"
   ]
  },
  {
   "source": [
    "The Monte carlo approximation to the variance of $\\theta$ is: "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "The Monte carlo approximation for the variance is 17.775810038188105\nThe true value for the mean is 18.0\n"
     ]
    }
   ],
   "source": [
    "print('The Monte carlo approximation for the variance is {}'.format(np.var(theta)))\n",
    "print('The true value for the mean is {}'.format(a / (b**2)))"
   ]
  },
  {
   "source": [
    "### Calculating probabilities\n",
    "\n",
    "One extremely useful example of an $h$ function is is the indicator $I_A(\\theta)$ where $A$ is some logical condition about the value of $\\theta$. To demonstrate, suppose $h(\\theta)=I_{[\\theta<5]}(\\theta)$, which will give a 1 if $\\theta < 5$ and return a 0 otherwise. What is $E(h(θ))$? This is the integral:\n",
    "\n",
    "$ \\int_0^\\infty I_{[\\theta<5]}(\\theta) p(\\theta) d\\theta = \\int_0^5 1 \\cdot p(\\theta) d\\theta + \\int_5^\\infty 0 \\cdot p(\\theta) d\\theta = P(\\theta < 5) \\, $\n",
    "\n",
    "It means we can approximate the probability that $θ<5$ by drawing many samples $θ^∗_i$, and approximating this integral with $\\frac{1}{m} \\sum_{i=1}^m I_{\\theta^* < 5} (\\theta_i^*)$. This expression is simply counting how many of those samples come out to be less than 5, and dividing by the total number of simulated samples.\n"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "The first 5 values of theta > 5 are: [False False False False False]\nThe first 5 values of theta are: [ 6.95464211 10.08906831  8.0512179  14.91576443  6.18135974]\nAn approximation to P(theta < 5) is: 0.4939\nThe true probability of P(theta < 5) is: 0.4963317257665017\n"
     ]
    }
   ],
   "source": [
    "# Indicator variable\n",
    "ind = theta < 5.0\n",
    "print('The first 5 values of theta > 5 are: {}'.format(ind[:5]))\n",
    "print('The first 5 values of theta are: {}'.format(theta[:5]))\n",
    "print('An approximation to P(theta < 5) is: {}'.format(np.mean(ind)))\n",
    "print('The true probability of P(theta < 5) is: {}'.format(rv.cdf(5)))"
   ]
  },
  {
   "source": [
    "Likewise, we can approximate quantiles of a distribution. If we are looking for the value $z$ such that $P(θ<z)=0.9$, we simply arrange the samples $θ^∗_i$ in ascending order and find the smallest drawn value that is greater than $90%$ of the others."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "The approximation of the 90th percentile of theta is 11.622035450808665\nThe true 90th percentile of theta is 11.669160509602287\n"
     ]
    }
   ],
   "source": [
    "q_theta = np.quantile(theta, 0.9)\n",
    "print('The approximation of the 90th percentile of theta is {}'.format(q_theta))\n",
    "print('The true 90th percentile of theta is {}'.format(rv.ppf(0.9)))"
   ]
  },
  {
   "source": [
    "### Monte Carlo error\n",
    "\n",
    "How good is an approximation by Monte Carlo sampling? Again we can turn to the CLT, which tells us that the variance of our estimate is controlled in part by m. For a better estimate, we want larger m.\n",
    "\n",
    "For example, if we seek $\\mathbb{E}(θ)$, then the sample mean $\\hat{θ}^∗$ approximately follows a normal distribution with mean $\\mathbb{E}(θ)$ and variance $\\frac{Var(θ)}{m}$, therefore, $\\hat{θ}^∗ \\sim \\mathcal{N}(\\mathbb{E}(θ), \\frac{Var(θ)}{m})$. The variance tells us how far our estimate might be from the true value. One way to approximate $Var(θ)$ is to replace it with the sample variance. The standard deviation of our Monte Carlo estimate is the square root of that, or the sample standard deviation divided by $\\sqrt{m}$. If $m$ is large, it is reasonable to assume that the true value will likely be within about two standard deviations of your Monte Carlo estimate."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set a random seed\n",
    "np.random.seed(seed = 32)\n",
    "\n",
    "a, b = 2, 1/3 # Gamma function parameters\n",
    "m = 10000 # Monte carlo sample size\n",
    "\n",
    "# Lambda is 1/scale\n",
    "rv = gamma(a, loc = 0., scale = 1/b)\n",
    "# sampling from gamma function\n",
    "theta = rv.rvs(m)"
   ]
  },
  {
   "source": [
    "Recall that the standard error is:\n",
    "\n",
    "$ \\sqrt{\\frac{\\hat{Var}(\\theta)}{m}}$"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "The standard error is: 0.04322709073070175\n"
     ]
    }
   ],
   "source": [
    "# Compute standard error\n",
    "se = np.std(theta) / np.sqrt(m)\n",
    "print('The standard error is: {}'.format(se))"
   ]
  },
  {
   "source": [
    "To create a confidence interval for the Monte Carlo approximation. We could look at, for example, two times the standard error. That is, we are reasonably confident, about 95% confident. That the Monte Carlo estimate for the expected value of theta is no more than this far from the true value of the expected value of theta. "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "A 0.95 confidecente interval for our Monte Carlo estimate is: 0.0864541814614035\n\nThe lower edge of the confidence interval is: 6.006200987492433\n\nThe upper edge of the confidence interval is: 6.179109350415241\n\n"
     ]
    }
   ],
   "source": [
    "print('A 0.95 confidecente interval for our Monte Carlo estimate is: {}\\n'.format(2 * se))\n",
    "\n",
    "print('The lower edge of the confidence interval is: {}\\n'.format(np.mean(theta) - 2 * se))\n",
    "print('The upper edge of the confidence interval is: {}\\n'.format(np.mean(theta) + 2 * se))\n",
    "\n",
    "# We are confident that the true mean is between the lower and upper interval showed below!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "An approximation to P(theta < 5) is: 0.4887\nThe true probability of P(theta < 5) is: 0.4963317257665017\n"
     ]
    }
   ],
   "source": [
    "# Indicator variable\n",
    "ind = theta < 5.0\n",
    "ind_mean = np.mean(ind)\n",
    "print('An approximation to P(theta < 5) is: {}'.format(ind_mean))\n",
    "print('The true probability of P(theta < 5) is: {}'.format(rv.cdf(5)))\n"
   ]
  },
  {
   "source": [
    "To obtain the Monte Carlo standard error for our Monte Carlo estimate. \n",
    "\n",
    "$ \\sqrt{\\frac{\\hat{Var}(I)}{m}}$"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "The standard error of the indicator is: 0.004998722936910987\nA 0.95 confidecente interval for our Monte Carlo estimate is: 0.009997445873821974\n\nThe lower edge of the confidence interval is: 0.47870255412617807\n\nThe upper edge of the confidence interval is: 0.498697445873822\n\n"
     ]
    }
   ],
   "source": [
    "se = np.std(ind) / np.sqrt(m)\n",
    "print('The standard error of the indicator is: {}'.format(se))\n",
    "\n",
    "print('A 0.95 confidecente interval for our Monte Carlo estimate is: {}\\n'.format(2 * se))\n",
    "\n",
    "print('The lower edge of the confidence interval is: {}\\n'.format(ind_mean - 2 * se))\n",
    "print('The upper edge of the confidence interval is: {}\\n'.format(ind_mean + 2 * se))"
   ]
  },
  {
   "source": [
    "### Example with Hierarchical model\n",
    "\n",
    "We can also obtain Monte Carlo samples from hierarchical models. As a simple example, let’s consider a binomial random variable where $y∣ϕ∼Bin(10,ϕ)$, and further suppose $ϕ$ is random (as if it had a prior) and is distributed beta $ϕ∼Beta(2,2)$. Given any hierarchical model, we can always write the joint distribution of $y$ and $ϕ$ as $p(y,ϕ)=p(y∣ϕ)p(ϕ)$ using the chain rule of probability. To simulate from this joint distribution, repeat these steps for a large number $m$:\n",
    "\n",
    "1. Simulate $ϕ^∗_i$ from its $Beta(2,2)$ distribution.\n",
    "2. Given the drawn $ϕ^∗_i$, simulate $y^∗_i$ from $Bin(10,ϕ^∗_i)$.\n",
    "\n",
    "This will produce m independent pairs of $(y^∗,ϕ^∗)_i$ drawn from their joint distribution. One major advantage of Monte Carlo simulation is that marginalizing is easy. Calculating the marginal distribution of p(y) = \\int_0^1 p(y, \\phi) d\\phi, might be challenging. But if we have draws from the joint distribution, we can just discard the $ϕ^∗_i$ draws and use the $y^∗_i$ as samples from their marginal distribution. This is also called the prior predictive distribution"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import beta\n",
    "from scipy.stats import binom\n",
    "\n",
    "# Params binomial \n",
    "n = 10\n",
    "# Params for betta\n",
    "a, b = 2, 2\n",
    "\n",
    "# Total draws 10000\n",
    "m = int(1e5)\n",
    "\n",
    "# Beta object\n",
    "rv_beta = beta(a, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "The first 5 samples of theta are: [0.32952162 0.15608715 0.32379823 0.59441233 0.48888113]\nThe first 5 samples of y star are: [4 2 9 8 6]\n"
     ]
    }
   ],
   "source": [
    "# Step 1, draw samples from beta distribution\n",
    "theta = rv_beta.rvs(m)\n",
    "# Step 2, draw samples from binomial using draws from beta\n",
    "rv_bin = binom(n, theta)\n",
    "y_star = rv_bin.rvs(m)\n",
    "print('The first 5 samples of theta are: {}'.format(theta[:5]))\n",
    "print('The first 5 samples of y star are: {}'.format(y_star[:5]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "No handles with labels found to put in legend.\n"
     ]
    },
    {
     "output_type": "display_data",
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     },
     "metadata": {}
    }
   ],
   "source": [
    "# Plotting the histogram of the random samples\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.hist(y_star, density=False, histtype='stepfilled', alpha=0.2)\n",
    "ax.legend(loc='best', frameon=False)\n",
    "plt.title('Histogram of Y*')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "{0: 3759, 1: 6974, 2: 9403, 3: 11251, 4: 12407, 5: 12660, 6: 12237, 7: 11162, 8: 9304, 9: 7016, 10: 3827}\n"
     ]
    }
   ],
   "source": [
    "# Count events\n",
    "unique, counts = np.unique(y_star, return_counts=True)\n",
    "print(dict(zip(unique, counts)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "{0: 0.03759, 1: 0.06974, 2: 0.09403, 3: 0.11251, 4: 0.12407, 5: 0.1266, 6: 0.12237, 7: 0.11162, 8: 0.09304, 9: 0.07016, 10: 0.03827}\nThe sum of all probabilies is: 1.0\n"
     ]
    }
   ],
   "source": [
    "# To obtain the probabilities, divide the counts per m\n",
    "p_counts = counts / m\n",
    "print(dict(zip(unique, p_counts)))\n",
    "print('The sum of all probabilies is: {}'.format(np.sum(p_counts)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "# Plotting the marginal distribution of y*\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.plot(p_counts, alpha=0.5, label = 'Monte Carlo Y*')\n",
    "ax.legend(loc='best', frameon=False)\n",
    "plt.title('Monte Carlo approximation of Y*')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "The marginal expected value of Y* is: 4.99863\n"
     ]
    }
   ],
   "source": [
    "# The marginal expected value of Y\n",
    "print('The marginal expected value of Y* is: {}'.format(np.mean(y_star)))"
   ]
  }
 ]
}